Neural network study of the nuclear ground-state spin distribution within a random interaction ensemble

The distribution of the nuclear ground-state spin in a two-body random ensemble(TBRE)was studied using a general classification neural network(NN)model with two-body interaction matrix elements as input features and the corresponding ground-state spins as labels or output predictions.The quantum many-body system problem exceeds the capability of our optimized NNs in terms of accurately predicting the ground-state spin of each sample within the TBRE.However,our NN model effectively captured the statistical properties of the ground-state spin because it learned the empirical regularity of the ground-state spin distribution in TBRE,as discovered by physicists.

Normalized Ground State Solutions of Nonlinear Choquard Equations with Nonconstant Potential

In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods.

Infinitely Many Solutions and a Ground-State Solution for Klein-Gordon Equation Coupled with Born-Infeld Theory

In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.

THE EXISTENCE AND CONCENTRATION OF GROUND STATE SIGN-CHANGING SOLUTIONS FOR KIRCHHOFF-TYPE EQUATIONS WITH A STEEP POTENTIAL WELL

In this paper,we consider the nonlinear Kirchhoff type equation with a steep potential well−(a+b∫_(R)^(3)|∇u|^(2 )dx)Δu+λV(x)u=f(u)in R^(3),where a,b>0 are constants,λ is a positive parameter,V∈C(R3,R)is a steep potential well and the nonlinearity f∈C(R,R)satisfies certain assumptions.By applying a signchanging Nehari manifold combined with the method of constructing a sign-changing(PS)C sequence,we obtain the existence of ground state sign-changing solutions with precisely two nodal domains when λ is large enough,and find that its energy is strictly larger than twice that of the ground state solutions.In addition,we also prove the concentration of ground state sign-changing solutions.

Structure and analytical potential energy function for the ground state of the BC^x （x=0, -1）

In this paper, the electronic states of the ground states and dissociation limits of BC and BC- are correctly determined based on group theory and atomic and molecular reaction statics. The equilibrium geometries, harmonic frequencies and dissociation energies of the ground state of BC and BC- are calculated by using density function theory and quadratic CI method including single and double substitutions. The analytical potential energy functions of these states have been fitted with Murrell-Sorbie potential energy function from our ab initio calculation results. The spectroscopic data （αe, ωe and ωeχe） of each state is calculated via the relation between analytical potential energy function and spectroscopic data. All the calculations are in good agreement with the experimental data.

Magnetic ground state of plutonium dioxide: DFT+U calculations

The magnetic states of the strongly correlated system plutonium dioxide(PuO_(2)) are studied based on the density functional theory(DFT) plus Hubbard U(DFT +U) method with spin–orbit coupling(SOC) included. A series of typical magnetic structures including the multiple-k types are simulated and compared in the aspect of atomic structure and total energy. We test LDA, PBE, and SCAN exchange–correlation functionals on PuO_(2) and a longitudinal 3k antiferromagnetic(AFM) ground state is theoretically determined. This magnetic structure has been identified to be the most stable one by the former computational work using the hybrid functional. Our DFT +U + SOC calculations for the longitudinal 3k AFM ground state suggest a direct gap which is in good agreement with the experimental value. In addition, a genetic algorithm is employed and proved to be effective in predicting magnetic ground state of PuO2. Finally, a comparison between the results of two extensively used DFT +U approaches to this system is made.

THE EXISTENCE OF GROUND STATE NORMALIZED SOLUTIONS FOR CHERN-SIMONS-SCHRODINGER SYSTEMS

In this paper,we study normalized solutions of the Chern-Simons-Schrödinger system with general nonlinearity and a potential in H^(1)(ℝ^(2)).When the nonlinearity satisfies some general 3-superlinear conditions,we obtain the existence of ground state normalized solutions by using the minimax procedure proposed by Jeanjean in[L.Jeanjean,Existence of solutions with prescribed norm for semilinear elliptic equations,Nonlinear Anal.(1997)].

LIMIT BEHAVIOR OF GROUND STATES OF 2D BINARY BECS IN STEEP POTENTIAL WELLS

We study the ground states of attractive binary Bose-Einstein condensates with N particles,which are trapped in the steep potential wellsλV(x)inℝ2.We show that there exists a positive number N*such that if N>N*,the system admits no ground state for anyλ>0.Moreover,there exist two positive numbers,M*andλ*(N),such that if N<M*,then for anyλ>λ*(N),the system admits at least one ground state.Asλ→∞,for any fixed N<M*,we give a detailed description for the limit behavior of both positive and semi-trivial ground states.

EXISTENCE OF A GROUND STATE SOLUTION FOR THE CHOQUARD EQUATION WITH NONPERIODIC POTENTIALS

We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under some suitable assumptions,we prove the existence of a ground state solution of the equation.Additionally,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.

Sympathetic electromagnetically induced transparency ground state cooling of a~(40)Ca^(+)–~(27)Al^(+)pair in an~(27)Al^(+)clock

We report on electromagnetically induced transparency cooling of ^(40)Ca^(+)to sympathetically cool the threedimensional secular modes of motion in a ^(40)Ca^(+)–^(27)Al^(+)two-ion pair near the ground state.We observe simultaneous ground state cooling across all radial modes and axial modes of a ^(40)Ca^(+)–^(27)Al^(+)ion pair,occupying a broader cooling range in frequency space over 3 MHz.The cooling time is observed to be less than 1 ms.The mean phonon number and heating rates of all motional modes are measured.This study is not only an important step for reducing the secular motion time-dilation shift uncertainty and uptime ratio of ^(27)Al^(+)optical clock,but also essential for high-fidelity quantum simulations and quantum information processors using trapped ions.

The Existence of Ground State Solutions for Schrödinger-Kirchhoff Equations Involving the Potential without a Positive Lower Bound

In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R2 and f has critical exponential growth. By using a version of Trudinger-Moser inequality and variational methods, we obtain the existence of ground state solutions for this problem.

Ground-state energy of beryllium atom with parameter perturbation method

We present a perturbation study of the ground-state energy of the beryllium atom by incorporating double parameters in the atom＇s Hamiltonian. The eigenvalue of the Hamiltonian is then solved with a double-fold perturbation scheme,where the spin-spin interaction of electrons from different shells of the atom is also considered. Calculations show that the obtained ground-state energy is in satisfactory agreement with experiment. It is found that the Coulomb repulsion of the inner-shell electrons enhances the effective nuclear charge seen by the outer-shell electrons, and the shielding effect of the outer-shell electrons to the nucleus is also notable compared with that of the inner-shell electrons.

Ground response and failure mechanism of gob-side entry by roof cutting with hard main roof

This study is the result of long-term efforts of the authors’team to assess ground response of gob-side entry by roof cutting(GSERC)with hard main roof,aiming at scientific control for GSERC deformation.A comprehensive field measurement program was conducted to determine entry deformation,roof fracture zone,and anchor bolt(cable)loading.The results indicate that GSERC deformation presents asymmetric characteristics.The maximum convergence near roof cutting side is 458 mm during the primary use process and 1120 mm during the secondary reuse process.The entry deformation is closely associated with the primary development stage,primary use stage,and secondary reuse stage.The key block movement of roof cutting structure,a complex stress environment,and a mismatch in the supporting design scheme are the failure mechanism of GSERC.A controlling ideology for mining states,including regional and stage divisions,was proposed.Both dynamic and permanent support schemes have been implemented in the field.Engineering practice results indicate that the new support scheme can efficiently ensure long-term entry safety and could be a reliable approach for other engineering practices.

Cell Evolutionary Algorithm: a New Optimization Method on Ground-State Energy of the Atomic

The purpose of this paper is to present a new general approach to solve ground-state energies of the double-electron systems in a uniform magnetic field, in which the basic element of evolution is the set in the solution space, rather than the point. The paper defines the Cell Evolutionary Algorithm, which implements such a view of the evolution mechanism. First, the optimal set in which the optimal solution may be obtained. Then this approach applies the embedded search method to get the optimal solution. We tested this approach on the atomic structure, and the results show that it can improve not only the efficiency but also the accuracy of the calculations as it relates to this specific problem.

Energy Emissions Profile and Floating Solar Mitigation Potential for a Malaysia’s State

The establishment of the National Low Carbon City Master Plan(NLCCM)by Malaysia’s government presents a significant opportunity to minimize carbon emissions at the subnational or local scales,while simultaneously fostering remarkable economic potential.However,the lack of data management and understanding of emissions at the subnational level are hindering effective climate policies and planning to achieve the nationally determined contribution and carbon neutrality goal.There is an urgent need for a subnational emission inventory to understand and manage subnational emissions,particularly that of the energy sector which contribute the biggest to Malaysia’s emission.This research aims to estimate carbon emissions for Selangor state in accordance with the Global Protocol for Community-Scale Greenhouse Gas Emission Inventories(GPC),for stationary energy activities.The study also evaluates the mitigation potential of Floating Solar Photovoltaic(FSPV)proposed for Selangor.It was found that the total stationary energy emission for Selangor for the year 2019 was 18,070.16 ktCO2e,contributed the most by the Manufacturing sub-sector(40%),followed by the Commercial and Institutional sub-sector;with 82%contribution coming from the Scope 2 emission.The highest sub-sector of Scope 1 emissions was contributed by Manufacturing while Scope 2 emissions from the Commercial and Institutional.Additionally,the highest fuel consumed was natural gas,which amounted to 1404.32 ktCO2e(44%)of total emissions.The FSPV assessment showed the potential generation of 2.213 TWh per year,by only utilizing 10%of the identified available ponds and dams in Selangor,equivalent to an emission reduction of 1726.02 ktCO2e,offsetting 11.6%Scope 2 electricity emission.The results from the study can be used to better evaluate existing policies at the sub-national level,discover mitigation opportunities,and guide the creation of future policies.

Ultralow operating voltage for energy conversion performance in Hf_(1-x)Zr_(x)O_(2) thin films

Emerging ferroelectric and antiferroelectric HfO_(2)-based thin films are attractive candidates for energy conversion and storage applications. In this work, the polar phase transformation between tetragonal and orthorhombic phases associated with ferroelectric or antiferroelectric behaviors is utilized to manipulate the electrocaloric cooling and energy storage performances in Zr-doped, woken up HfO_(2) ultrathin films. A giant electrocaloric temperature change of up to 11.85 K in Hf_(0.5)Zr_(0.5)O_(2) with the morphotropic phase boundary (MPB) state and a high energy storage density of 39.34 J/cm3 in the tetragonal phase-dominant Hf0.25Zr0.75O2 system are obtained. More interestingly, contrary to overdoping and excessive electric fields, an appropriate Zr concentration of 0.5 and an applicable driving field of 1.91 MV/cm are desired for the electrocaloric effect, resulting in an ultralow operating voltage as low as 1.3 V in this 6.8 nm thick Hf_(0.5)Zr_(0.5)O_(2) film. These findings illustrate that the structural design strategy is a visible method for achieving optimal energy-related behaviors and highlight the great possibilities for building future energy-related devices.

Simulation of Start-Up Process of Turbofan Engine Based on Full-State Characteristics of Fan

Difficulties in obtaining component characteristics in the sub-idle state of rotor constrain the simulation capabilities of ground and windmill start-up processes for turbofan engines.This paper proposes a backbone feature method based on conventional characteristics parameters to derive the full-state characteristics of fan.The application of the fan’s full-state characteristics in component-level model of turbofan engine enables zero-speed iterative simulation for ground start-up process and windmill simulation for windmill start-up process,thereby improving the simulation capability of sub-idle state during turbofan engine start-up.

Quasiclassical Trajectory Study of Collisional Energy Transfer between Highly Excited C_6F_6 and N_2 ,O_2 and Ground State C_6F_6

Quasiclassical trajectory calculation (QCT) is used frequently for studying collisional energy transfer between highly vibrationally excited molecules and bath gases. In this paper, the QCT of the energy transfer between highly vibrationally excited C6F6 and N2 ,O2 and ground state C6F6 were performed. The results indicate that highly vibrationally excited C6F6 transferred vibrational energy to vibrational distribution of N2, O2 and ground state C6F6, so they are V-V energy transfer. Especially it is mainly V-V resonance energy transfer between excited C6F6 and ground state C6F6, excited C6F6 transfers more vibrational energy to ground state C6F6 than to N2 and O2 . The values of QCT , -〈DEvib〉of excited C6F6 are smaller than those of experiments.

Full-Dimensional Potential Energy Surfaces of Ground(X^(2)A′)and Excited(A^(2)A″)Electronic States of HCO and Absorption Spectrum

In this work,high-fidelity full-dimensional potential energy surfaces(PESs)of the ground(X^(2)A′)and first doublet excited(A^(2)A″)electronic states of HCO were constructed using neural network method.In total,4624 high-level ab initio points have been used which were calculated at Davidson corrected internally contracted MRCI-F12 level of theory with a quite large basis set(ACV5Z)without any scaling scheme.Compared with the results obtained from the scaled PESs of Ndenguéet al.,the absorption spectrum based on our PESs has slightly larger intensity,and the peak positions are shifted to smaller energy for dozens of wavenumbers.It is indicated that the scaling of potential energy may make some unpredictable difference on the dynamical results.However,the resonance energies based on those scaled PESs are slightly closer to the current available experimental values than ours.Nevertheless,the unscaled high-level PESs developed in this work might provide a platform for further experimental and theoretical photodissociation and collisional dynamic studies for HCO system.

Modified Atomic Orbital Calculations of Energy of the(2s^(2)^(1)S)Ground-State,the(2p^(2)^(1)D);(3d^(2)^(1)G)and(4f^(2)^(1)I)Doubly Excited States of Helium Isoelectronic Sequence from H-to Ca^(18+)

We report in this paper the ground-state energy 2s^(2)^(1)S and total energies of doubly excited states 2p^(2)^(1)D,3d^(2)^(1)D,4f^(2)^(1)I of the Helium isoelectronic sequence from H-to Ca^(18+).Calculations are performed using the Modified Atomic Orbital Theory(MAOT)in the framework of a variational procedure.The purpose of this study required a mathematical development of the Hamiltonian applied to Slater-type wave function[1]combining with Hylleraas-type wave function[2].The study leads to analytical expressions which are carried out under special MAXIMA computational program.This first proposed MAOT variational procedure,leads to accurate results in good agreement as well as with available other theoretical results than experimental data.In the present work,a new correlated wave function is presented to express analytically the total energies for the 2s21S ground state and each doubly 2p^(2)^(1)D,3d^(2)^(1)D,4f^(2)^(1)I excited states in the He-like systems.The present accurate data may be a useful guideline for future experimental and theoretical studies in the(nI^(2))systems.